Builder's Old Measurement - History and Derivation

History and Derivation

The first tax on the hire of ships in England was levied by King Edward I in 1303 based on tons burthen. Later, King Edward III levied a tax of 3 shillings on each "tun" of imported wine, equal to £58.35 today (using the last year of Edward III's reign, 1377, as the base year). At that time a "tun" was a wine container of 252 gallons weighing about 2,240 lb (1,020 kg), a weight known today as a long ton or imperial ton. In order to estimate the capacity of a ship in terms of 'tun' for tax purposes, an early formula used in England was:

where:

• Length is the length (undefined), in feet
• Beam is the beam, in feet.
• Depth is the depth of the hold, in feet below the main deck.

The numerator yields the ship's volume expressed in cubic feet.

If a "tun" is deemed to be equivalent to 100 cubic feet, then the tonnage is simply the number of such 100 cubic feet 'tun' units of volume.

• 100 the divisor is unitless, so tonnage would be expressed in 'ft³ of tun'.

In 1678 Thames shipbuilders used a method assuming that a ship's burden would be 3/5 of its displacement. Since tonnage is calculated by multiplying length × beam × draft × block coefficient, all divided by 35 ft³ per ton of seawater, the resulting formula would be:

where:

• Draft is estimated to be half of the beam.
• Block coefficient is based on an assumed average of 0.62.
• 35 ft³ is the volume of one ton of sea water.

Or by solving :

In 1694 a new British law required that tonnage for tax purposes be calculated according to a similar formula:

This formula remained in effect in until the Builder's Old Measurement rule was put into use in 1720, and then by Parliamentary law in 1773.